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CfE Higher Physics Unit 1
Our Dynamic Universe
Higher Physics
Our Dynamic Universe
Thrust
Unbalanced
Force
Air
Resistance
Weight
Pupil Notes
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CfE Higher Physics Unit 1
Our Dynamic Universe
Equations of Motion
Links to National 5: Speed, Distance and Time; Acceleration; Scalers and
Vectors.
The Equations of Motion are used to determine a quantity relation to a moving
object when the speed does not remain constant. There are three equations of
motion that must be considered.
Equation 1:
We use the acceleration formula from National 5 are re-arrange it slightly
a
vu
t
v  u  at
Equation 2:
Consider a moving object which does not start at rest and the speed is
continually increasing.
We are able to calculate the
displacement travelled by calculating
the area under the graph.
1
v  u t
2
at  (v  u ) (Equation 1)
1
s  ut  att
2
s  ut 
s  ut 
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1 2
at
2
CfE Higher Physics Unit 1
Our Dynamic Universe
Equation 3:
We begin with Equation 1 in the Higher Physics form and square it. The
brackets are then expanded.
v  u  at
v  u  at u  at 
2
v  u 2  uat  uat  a 2t 2
v 2  u 2  2uat  a 2t 2
1


v 2  u 2  2a ut  at 2 
2 

2
Use Equation 2
v 2  u 2  2as
Creating an information bank at the side of the page when doing a calculation
allows for easier determination of which equation of motion to use.
s = Displacement (m)
u = Initial Velocity (ms-1)
v = Final Velocity (ms-1)
a = Acceleration (ms-2)
t = Time (s)
Vector rules:




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Usually consider an object moving to the right/up
as positive and an object moving to the left/down
as negative unless stated initially.
When an object is moving vertically, gravitational
field strength will act as the acceleration value.
When an object moves up, it is going against
gravity so the value of acceleration will be
negative. When an object is falling, that is a
downwards direction so acceleration is negative.
In short, when moving vertically, acceleration is
always negative!
CfE Higher Physics Unit 1
Our Dynamic Universe
Motion Time Graphs
Link to National 5: Speed time graphs; Acceleration; Vectors
In Higher we must consider all aspects of motion when we display then in graphs
– Velocity, Displacement and Acceleration.
Velocity-Time Graphs
Constant Velocity
Increasing Velocity
with Constant
Acceleration
Decreasing
Velocity with
Constant
Deceleration
As with National 5, the displacement travelled by an object can be calculated
by using the area under the graph. Any area which lies below the x axis must be
considered a negative value when calculating the total displacement.
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CfE Higher Physics Unit 1
Our Dynamic Universe
Displacement-Time Graphs
The gradient of the line on a displacement-time graph is equal to the velocity of
the object.
Acceleration-Time Graphs
At Higher, acceleration will always be constant.
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CfE Higher Physics Unit 1
Our Dynamic Universe
Bouncing Ball example
B
A
D
C
A – Ball is released from a height.
B – Ball reaches maximum velocity
C - Ball rebounds off the ground.
D – Ball reaches maximum height after rebound
When a velocity-time/acceleration-time graph falls below the x-axis, this can
indicate that the object is slowing down OR that a change in direction has taken
place. In both cases the magnitude value for velocity, acceleration or
displacement will be negative.
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CfE Higher Physics Unit 1
Our Dynamic Universe
Forces
Link to National 5 – Unbalanced Forces; Acceleration
Newton’s First Law states that an object will remain at rest or travel at a
constant speed unless acted upon by an unbalanced force.
Newton’s Second Law states that the force applied to a mass is directly
proportional to the acceleration of the mass.
F  ma
Tension
Tension can be created by one object pulling another, or by an object hanging
from a surface.
The box remains stationery will hanging from the
ceiling. This means that the tension in the rope is
equal to the weight of the object.
T  mg
T  9.8  6
T  58.8 N
When one object is pulling another, more steps must be taken in order for the
tension in the rope to be found. Take the example below to find the tension in
the rope.
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CfE Higher Physics Unit 1
2·0 kg
Our Dynamic Universe
4·0 kg
12 N
1. Consider the total mass in order to calculate the acceleration of the whole
system
F  ma
12  6a
12
a   2ms 2
6
2. Consider the mass that comes after the tension rope ONLY. This mass is
travelling with the same acceleration but is the mass creating tension.
F  ma
F  2 x2
F  4N
Weight in a lift
When you step on a set of bathroom scales, the reading provided is
actually the reaction force of the scales pushing back against your weight.
When stationary the reaction force is equal to your weight. If you
accelerate whilst standing on scales, the reading will be different.
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CfE Higher Physics Unit 1
Our Dynamic Universe
An unbalanced force will act on the lift in the direction in which it is
travelling. Weight will always be acting down; reaction force up.
Accelerating up in a lift
Reaction
Reaction and Unbalanced Force are acting in
the same direction, but opposite to the
weight:
ma = R – mg
R = ma +mg
Fun
When accelerating upwards, you appear
heavier.
Weight
Accelerating down in a lift
Reaction
Weight and Unbalanced Force are acting in
the same direction, but opposite to the
reaction force:
ma = mg - R
R = mg - ma
Fun
When accelerating downwards, you appear
lighter.
Weight
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CfE Higher Physics Unit 1
Our Dynamic Universe
Components of Force
If a force acts on an object at an angle, the force can be split up into
horizontal and vertical components.
The forces are calculated using trigonometry (SOHCAHTOA)
FH = F cos Θ
FH = 4 cos 26
FH = 3.6 N
FV = F sin Θ
FV = 4 sin 26
FV = 1.8 N
Do not expect the horizontal and vertical components to add up to the original
force being applied.
This same rule can be applied for masses sitting on a slope.
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Our Dynamic Universe
mg sin Θ
Component of weight into the slope = mg cos Θ
Component of weight down the slope =
Example:
A box rests on a slope as shown in the diagram below.
The force of friction acting on the box as it moves down the hill remains
constant at 1.2 N. Calculate:
(a)
(b)
The perpendicular and parallel components of weight.
The acceleration of the block down the slope.
(a) Perpendicu lar  mg cos  2  9.8 cos30  17 N
Parallel
 mg sin   2  9.8 sin 30  9.8 N
(b) Fun  Parallel - Friction
Fun  9.8  1.2  8.6 N
a
Fun 8.6

 4.3ms  2
a
2
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CfE Higher Physics Unit 1
Our Dynamic Universe
Momentum and Impulse
Link to National 5 – Scalers and Vectors, Conservation of Energy
The conservation of linear momentum states that in the absence of external
forces, the total momentum of a system before a collison is equal to the total
momentum after the collison.
All moving objects have momentum – the number calculated is basically an
indicator as to how easy or difficult it will be to stop the moving object.
The momentum is described as a product of an object’s mass and velocity. Take
the following examples:
Trolley
Mass = 5 kg
Velocity = 0.5 ms-1
Tanker
Mass = 10 x 107 kg
Velocity = 0.01 ms-1
p  mv
p  5  0 .5
p  2.5kgms 1
p  mv
p  10 x10 7  0.01
p  1x10 6 kgms1
Bullet
Mass = 0.01 kg
Velocity = 500 ms-1
p  mv
p  0.01  500
p  5kgms1
So even though the trolley has a greater mass than the bullet and greater
velocity than the tanker, it has the overall smallest momentum and would be
easiest to stop!
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CfE Higher Physics Unit 1
Our Dynamic Universe
Collisions and Explosions
Momentum is a vector quantity as it contains a velocity value – therefore
direction is very important!!!! Always take an object going to the right as a
positive velocity and to the left as a negative velocity. Take each object
individually intially, then consider what is happening on either side of the
collision. Consider the following examples:
Before – Separate; After – Separate
m1
m2
u1
m1
u2 = 0
m1
v1
v2
Momentum Before  Momentum After
m1u1  m2 u 2  m1v1  m2 v2
Before – Separate; After – Together
m1
m2
u1
m1
u2 = 0
m2
v
Momentum Before  Momentum After
m1u1  m2 u 2  m1  m2 v
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Before – Together; After – Separate (Explosion)
m1
m2
m1
u=0
m1
v1
v2
Momentum Before  Momentum After
m1  m2 u   m1v1   m2 v2
Negative sign only indicates a
different direction – not that it
is slowing down!
Kinetic Energy and Momentum
Even though kinetic energy and momentum are both linked to movement, they
are not directly linked to each other. Consider the following examples:
The above boxes all have the same momenta but different kinetic energies. If
the momentum and kinetic energy are the same it is entirely coincidental!!
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CfE Higher Physics Unit 1
Our Dynamic Universe
Elastic and Inelastic Collisions
A collision can be deemed elastic or inelastic by whether the kientic energy of
the system is conserved after a collision. Tackle this in a similar manner when
completing momentum calculations – consider all objects’ energies individually,
then before and after the collision, then the system as a whole.
Total Kinetic Energy Before Collision = Total Kinetic Energy After Collision
Collision is Elastic
Total Kinetic Energy Before Collision ≠ Total Kinetic Energy After Collision
Collision is Inelastic
In reality, all collisions are inelastic as some kinetic energy will be transformed
into heat or sound energy.
Example so far: Calculate the velocity after the collision and determine
whether the collision is elastic or inelastic.
Momentum Before  Momentum After
m1u1   m2u 2   mv
2  3  5  1  7v
6  5  7v
1  7v
1
v  0.14 ms or 0.14 ms 1 to the right
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CfE Higher Physics Unit 1
Our Dynamic Universe
Kinetic Energy Before
1
1
2
2
Ek  m1u1  m2 u 2
2
2
Ek  0.5  2  3  3  0.5  5  1  1
Ek  11.5 J
Kinetic Energy After
1
Ek  mv 2
2
E k  0.5  7  0.14  0.14
Ek  0.07 J
Ek Before  Ek After
Collision is Inelastic
Impulse
Impulse is described as the length of time a force is applied to an object.
Impulse  Ft
This impulse will cause an object’s speed to change, and therefore change the
object’s momentum.
Impulse  Change in Momentum  mv  mu
As the impulse in both statements is the same, we can finalse our equation:
Ft  mv  mu
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Our Dynamic Universe
Force-Time Graphs
Similar to a velocity-time graph, another value can be found from a force-time
graph. The area under the force-time graph is equal to the impulse.
In these cases, time is usually a very small value and is often given in
milliseconds.
A force-time graph can also show whether the object being hit is soft or hard,
for example. Soft objects remain in contact for longer after being struck so
therefore the force is not as sudden.
Force (N)
Hard golf ball
Soft sponge ball
Time (ms)
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Our Dynamic Universe
Projectiles
Links to National 5: Projectiles, Acceleration, Conservation of Energy
When an object is released, it will be classed as a projectile until it reaches the
ground. Projectiles can travel horizontal or vertical. In Higher, we will look at
projectiles launched at an angle, as well as horizontally and vertically.
The equations of motion are used to calculate certain features of a projectile,
and certain rules remain the same. Units remain the same as before also.
Vertical Motion
v  u  at
1
s  ut  at 2
2
2
2
v  u  2as
Horizontal Motion
d  vt
Gravity will act as the ‘acceleration’ value for vertical movement = -9.8ms-2.
For projectiles launched with speed at an angle to the ground, the horizontal
and vertical components of that speed can be found.
u
Horizontal Component
u H  u cos
uV
Vertical Component
u v  u sin 
Θ
uH
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CfE Higher Physics Unit 1
Our Dynamic Universe
Projectiles launched at an angle will always follow a curved path. Split the path
of the projectile in two – from start to highest point, then highest point to end
– when looking at the vertical motion.
Horizontal motion remains constant throughout. When an object reaches
maximum height, it will momentarily stop before falling back to Earth. This
results in the final velocity for the first half/initial speed for second half of
the journey to be constant. It will take half the total time to reach max height.
Example:
A golfer strikes a ball at an angle of 25° to the ground and with a speed of 60
ms-1. The ball lands 6s later. Calculate:
(a)
(b)
(c)
The horizontal and vertical components of speed.
The range of the ball
The maximum height of the ball
(a) u H  u cos  60 cos 25  54.4ms 1
uV  u sin   60 sin 25  25.4ms 1
(b) v  54.4
t 6
s  vt
s  54.5  6
s  327 m
(c) u  25.4
1
s  ut  at 2
2
v0
a  9.8
t 3
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v 2  u 2  2as
1

s  25.4  3    9.8  9 
2

s  76.2  44.1
s  32.1m
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0  645 .16   2  9.8  s 
 645 .16  19.6 s
s  32 m
CfE Higher Physics Unit 1
Our Dynamic Universe
Gravitation
Mass and weight are two things that can cause confusion in Physics. Mass is
the amount of matter that an object consists of, whereas weight is a force
pulling that object down to the ground. This force is caused by a
gravitational pull.
There is always a gravitational pull between two masses – between two people
for example. This additional gravitational pull between two objects is never
felt as we are standing on the Earth – compared to a person, the Earth is
MASSIVE!!
Newton devised an equation to calculate the attractive force between two
masses that are a certain distance apart.
F
GM1 M 2
r2
G = Universal Gravitational Constant (6.67 x 10-11 Nm2kg-2)
M1 and M2 = Mass of objects (kg)
r = Distance between the objects (m)
Example: What is the gravitational force between a man of mass 80kg and
the Earth?
GM 1 M 2
r2
11
6.67 x10  80  6 x10 24
F
6.4 x10 6 2
F  781 .6 N
F
Comparing to W = mg = 80 x 9.8 = 784N
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Mass of
Earth
Radius of Earth
CfE Higher Physics Unit 1
Our Dynamic Universe
Special Relativity
Albert Einstein was the first person to fully consider that travelling at the
speed of light can alter space time – this was fully discussed in his Special
Theory of Relativity. The theory states that, in reality, nothing of mass
would be able to travel at the speed of light as the mass of the object would
become infinitely large. Only photons of light can travel at this speed.
Theoretically travelling close the speed of light (90% of the value) can also
have an effect on how an object is perceived by an observer – whether it be
how large the object is or how long it takes to pass by.
Time Dilation
An observer on Earth is looking at a space craft in space orbiting a planet.
The observer and the space craft are in different frames of reference and
the space craft is travelling close to the speed of light. To the observer, the
time it takes for the space craft to make one orbit will appear much longer
than the time it actually takes to orbit. This is known as time dilation.
Example: You leave earth and your twin to go on a space mission. You are in a
spaceship travelling at 90% the speed of light and you go on a journey that
lasts 20 years. When you get back you will find that 46 years will have
elapsed on Earth. Your clock will have run slowly compared to one on Earth,
however as far as you were concerned the clock would have been working
correctly on your spaceship, so for you only 20 years have elapsed. That is
because the space craft and Earth are two different frames of reference.
t'
t
v
1  
c
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t’ = Time outside observer’s frame of reference (s)
t = Time inside observer’s frame of reference (s)
v = Speed of object being observed (ms-1)
c = Speed of light (3 x 108 ms-1)
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CfE Higher Physics Unit 1
Our Dynamic Universe
Length Contraction
An observer on Earth is looking at a space craft in space orbiting a planet.
The observer and the space craft are in different frames of reference and
the space craft is travelling close to the speed of light. To the observer, the
length of spacecraft appears to be much shorter than the length it was when
the space craft was on Earth. The spacecraft in reality has not gotten any
smaller. This is known as length contraction.
v
l' l 1   
c
l’ = Length outside observer’s frame of reference (m)
l = Length inside observer’s frame of reference (m)
v = Speed of object being observed (ms-1)
c = Speed of light (3 x 108 ms-1)
2
Example: A spacecraft of length 270m is travelling at 0.83c (2.5x108) ms-1.
It takes 35 minutes to orbit a distance planet. Calculate the length of the
spacecraft and the time of orbit relative to an observer on Earth.
t'
2
v
l' l 1   
c
2


0
.
83
c



l '  270   1  


 c  

l '  270  1  0.6889
l '  270  0.55

t'
2
v
1  
c
2100
2
 0.83c 
1 

 c 
2100
t'
0.55
t '  3818 .2 s or 63 min

l '  150 .6m
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CfE Higher Physics Unit 1
Our Dynamic Universe
The Expanding Universe
The Doppler Effect
A lot people will have heard of the
term “the Doppler effect” from Dr.
Sheldon Cooper.
But what does it actually mean?
The Doppler Effect is the apparent change in frequency of a sound when the
source of the sound is moving away or towards a stationary observer. The
frequency of the sound does not actually change as only the source can
change the frequency.
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Our Dynamic Universe
 v
f o  f s 
 v  vs
These are very easy to
get mixed up!!!!



fo = Frequency heard by observer
fs = Frequency emitted by the source
v = Speed of Sound in air (340 ms-1)
vs = Speed of the source
What about the ± sign? This has got to do with whether the train is coming
towards or away from the observer. Best way to remember:
 Coming towards  Distance getting less  Subtract
 Moving away  Distance getting bigger  Add
Example: A train is travelling towards a station at a speed of 17 ms-1. To
alert passengers of its arrival, a siren is emitted with a frequency of 280 Hz.
Calculate the frequency heard by the passengers waiting.
 v 

f o  fs 
v

v

s 
 340 
f o  280

 340  17 
f o  280  1.05
f o  294 Hz
Redshift
The universe is expanding – and it is doing so at an accelerated rate. This
means that distance objects we can see (out with our Solar System) are
moving away from us at a fast rate. This expansion cause the light we see
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CfE Higher Physics Unit 1
Our Dynamic Universe
from a distant star to actually be a different colour from the light being
emitted. This is known as Redshift.
Redshift means that the light emitted from a distant object that is moving
away from us appears to “shift” towards the red end of the spectrum. It
does NOT mean that the light will turn red! the further away an object is,
the more it “shifts” to the red end of the spectrum.
By how much the light has moved towards the red end of the spectrum can
be determined with the following equation:
z
observed  rest
rest
z is the red shift factor. It is a number (so no units) that determines how
much the light has “shifted”. As the light being observed on Earth will always
be longer than the light being emitted, you cannot get a negative redshift
factor.
If the shift factor is negative, the light has actually moved towards the
violet/blue end of the spectrum – this is known as Blueshift.
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Our Dynamic Universe
The redshift factor can also be used to calculate at what speed the object is
moving away from Earth.
z
v
c
As redshift is a ratio between wavelength observed and wavelength emitted,
it can also be used as a ratio between the speed of the object and the speed
of light.
Example: A distant galaxy emits a photon of light with wavelength 570 nm. A
student on Earth observes this photon as having a wavelength of 597 nm.
Calculate the redshift value and the speed of the distant galaxy.
z
z
observed  rest
rest
597  570 
570
z  0.05
v
c
v  zc  0.05  3 x10 8
z
v  1.42 x10 7 ms 1
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Our Dynamic Universe
Hubble’s Law
In 1929, the astronomer Edwin Hubble announced that other galaxies are
moving away from us and the further a galaxy is from us the faster it is
moving away.
Hubble developed an equation to help determine how quickly a distant galaxy
is moving away from us.
v  Hod
v = Speed of the galaxy
Ho = Hubble’s constant (2.3 x 10-18 s-1)
d = Distance to galaxy
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CfE Higher Physics Unit 1
Our Dynamic Universe
The Big Bang Theory
Certain areas of astronomy and astrophysics are still not widely known about
and continued to be studied now. Scientists at institutes such as CERN and
ITER continually work to understand why the universe was created in the
way that it was.
Dark Matter and Dark Energy
‘It’s a fairly embarrassing situation to admit that we can’t find 90 per cent
of the universe’ – Astronomer B. Margon
Repeated measurements of the masses of galaxies lead to the conclusion
that 90% of the universe is matter in a form that cannot be seen – dark
matter.
Recent measurements of the expansion rate of the Universe found that the
expansion is actually speeding up.
There is something that overcomes the force of gravity – dark energy.
Dark energy is now believed to make up most of the total content of the
universe.
Temperature of Stars
As well as using the colour of light to determine how fast objects are moving
away from us, the colour of light can also be used to determine how hot
closer stars are.
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Our Dynamic Universe
Our own Sun is a relatively cool star in the grand scheme of things. The
temperature of a star also has a link as to how bright (luminous) the star is
also.
There are several sub categories of stars, including red giants and white
dwarfs.
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Our Dynamic Universe
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